📗 [4 points] Consider a Linear Threshold Unit (LTU) perceptron with initial weights \(w\) = and bias \(b\) = trained using the Perceptron Algorithm. Given a new input \(x\) = and \(y\) = . Let the learning rate be \(\alpha\) = , compute the updated weights, \(w', b'\) = :

📗 Answer (comma separated vector): . Calculate

📗 [1 points] Move the point and change the learning rate to see the derivatives (slope of tangent line) of the function \(x^{2}\). Find an initial point + learning rate combination so that gradient descent will not find the global minimum.

📗 [4 points] Given the following neural network that classifies all the training instances correctly. What are the labels (0 or 1) of the training data? The activation functions are LTU for all units: \(1_{\left\{z \geq 0\right\}}\). The first layer weight matrix is , with bias vector , and the second layer weight vector is , with bias

📗 Answer (comma separated vector): . Calculate

📗 [1 points] Transform the points (using the Quadratic Square-x1 Square-x2 feature map) and move the plane such that the plane separates the two classes.

📗 [4 points] "It" has a house with many doors. A random door is about to be opened with equal probability. Doors to have monsters that eat people. Doors to are safe. With sufficient bribe, Pennywise will answer your question "Will door 1 be opened?" What's the information gain (also called mutual information) between Pennywise's answer and your encounter with a monster?

📗 Answer: . Calculate

📗 [4 points] Given the following training data, which items will be classified correctly with the fold cross validation if NN (Nearest Neighbor) classifier with Manhattan distance is used. Break the tie (in distance) by using the instance with the smaller index. Check the items that are classified correctly in the table.

📗 [4 points] A convolutional neural network has input image of size x that is connected to a convolutional layer that uses a x filter, zero padding of the image, and a stride of 1. There are activation maps. (Here, zero-padding implies that these activation maps have the same size as the input images.) The convolutional layer is then connected to a pooling layer that uses x max pooling, a stride of (non-overlapping, no padding) of the convolutional layer. The pooling layer is then fully connected to an output layer that contains output units. There are no hidden layers between the pooling layer and the output layer. How many different weights must be learned in this whole network, not including any bias.

📗 Answer: . Calculate

📗 [4 points] Consider the problem of detecting if an email message is a spam. Say we use four random variables to model this problem: a binary class variable \(S\) indicates if the message is a spam, and three binary feature variables: \(C, F, N\) indicating whether the message contains "Cash", "Free", "Now". We use a Naive Bayes classifier with associated CPTs (Conditional Probability Table):

📗 Answer: . Calculate

📗 [4 points] Compute the context value of the word with \(q_{i} = x_{i} \cdot w_{q}\) = . You can enter the scaled dot products (optional) in the table and use the "Softmax" button to compute the soft attention weights.

📗 Answer: . Calculate

📗 [1 points] Please enter any comments including possible mistakes and bugs with the questions or your answers. If you have no comments, please enter "None": do not leave it blank.

📗 Answer: .